## Calculus (3rd Edition)

$$\frac{a}{3}$$
We have the derivative: $$f^{\prime}(x)=3x^{2}$$ Then at $x=a, m=f^{\prime}(a)=3a^{2}$. Hence, the tangent line is: \begin{aligned} \frac{y-y_{1}}{x-x_{1}} &=m \\ \frac{y-a^n}{x-a} &=3a^{2} \\ y &=3a^{2} (x-a)+a^3 \end{aligned} Since the tangent line intersects with the $x-$ axis at $x=0,$ then $Q$ has coordinates $(a-\frac{a}{3},0), R$ has coordinates $(a,0)$, and the subtangent is $$a-\left(a-\frac{a}{3}\right)=\frac{a}{3}$$